Measurement - the laboratory

Laboratory measurements determined the following roller lengths (in millimeters):
{402; 410; 412; 410; 413; 418; 405; 409; 410; 409}
Calculate arithmetic, geometric mean, mode, and median.

Correct answer:

a =  409.8
g =  409.7796
m₁ =  410
m₂ =  410

Step-by-step explanation:

$$\begin{gathered} n=10 \\ a=\frac{402+410+412+410+413+418+405+409+410+409}{n}=\frac{402+410+412+410+413+418+405+409+410+409}{10}=409.8 \end{gathered}$$

$g=(402\cdot 410\cdot 412\cdot 410\cdot 413\cdot 418\cdot 405\cdot 409\cdot 410\cdot 409{)}^{1/n}=\sqrt[10]{402\cdot 410\cdot 412\cdot 410\cdot 413\cdot 418\cdot 405\cdot 409\cdot 410\cdot 409}=409.7796$

$$\begin{gathered} sort:\{402,405,409,409,410,410,410,412,413,418\} \\ {m}_1=410 \end{gathered}$$

$m_2=m_1=410$

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